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Electric shocks A study carried out by R. Norell was designed to learn about the effect of small electrical currents on farm animals, with the eventual goal of understanding the effects of high-voltage power lines near farms. A total of m = 70 trials were carried out at each of six intensities, 0, 1, 2, 3, 4, and 5 mA (shocks on the order of 15 mA are painful for many humans, Dalziel, Lagen, and Thurston 1941). The data are given in the file shocks.txt with columns Intensity, number of trials m, which is always equal to 70, and Y, the number of trials out of m for which the response, mouth movement, was observed.
Draw a plot of the fraction responding versus Intensity. Then, fit the logistic regression with predictor Intensity, and add the fitted curve to your plot. Test the hypothesis that the probability of response is independent of Intensity, and summarize your conclusions. Provide a brief interpretation of the coefficient for Intensity.